{"id":"W2008229588","doi":"10.1016/s0377-0427(00)00274-0","title":"The role of Bell polynomials in integration","year":2001,"lang":"en","type":"article","venue":"Journal of Computational and Applied Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":25,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Connection (principal bundle); Polynomial; Bell polynomials; Expression (computer science); Simple (philosophy); Combinatorics; Pure mathematics; Discrete mathematics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006898299,0.0001091924,0.0003442183,0.0001076127,0.0000658971,0.00003481169,0.0001504484,0.00004308199,0.00001198304],"category_scores_gemma":[0.0003423297,0.00006992445,0.00006282867,0.0001385004,0.0001167344,0.0001076471,0.00004133196,0.0001466249,0.000002154931],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002733778,"about_ca_system_score_gemma":0.00003920038,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":6.948093e-7,"about_ca_topic_score_gemma":0.000004888376,"domain_scores_codex":[0.9984995,0.00001837047,0.0009463055,0.00006131019,0.0003553146,0.0001191833],"domain_scores_gemma":[0.9967886,0.002175555,0.0007343219,0.00008817673,0.000170266,0.00004307361],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00003546254,0.0001869554,0.00002937782,0.00007776744,0.0000275922,0.000001953746,0.001240733,0.0007445081,0.001370849,0.9909353,0.00008701573,0.005262543],"study_design_scores_gemma":[0.000349991,0.00003757609,0.0001072197,0.0001226525,0.00002561355,0.00008740832,0.002496671,0.00326883,0.002133773,0.9911052,0.0001979254,0.00006713052],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8319247,0.0006186751,0.1527254,0.0003674531,0.00007805736,0.000344019,0.000003518192,0.00001539769,0.0139227],"genre_scores_gemma":[0.8086225,0.000112919,0.1910034,0.00001255249,0.00006094724,0.000004877925,5.505506e-7,0.00001414725,0.0001680909],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03827797,"threshold_uncertainty_score":0.2851436,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02071540897554798,"score_gpt":0.2912383827240157,"score_spread":0.2705229737484677,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}